Abstract and concrete categories
Abstract and concrete categories
The general fuzzy filter approach to fuzzy topology, I
Fuzzy Sets and Systems - Special issue on mathematical aspects of fuzzy set theory
The general fuzzy filter approach to fuzzy topology, II
Fuzzy Sets and Systems - Special issue on mathematical aspects of fuzzy set theory
The theory of global fuzzy neighborhood structures part I—the general case
Fuzzy Sets and Systems
The theory of global fuzzy neighborhood structures. III: fuzzy uniform structures
Fuzzy Sets and Systems - Special issue on topics of the mathematics of fuzzy objects
On initial and final fuzzy uniform structures
Fuzzy Sets and Systems - Topology
On initial and final L-topological groups
Fuzzy Sets and Systems
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This paper introduces and studies the notion of global L-neighborhood group which is defined as a group equipped with a global L-neighborhood structure in sense of Gahler et al. such that both the binary operation and the unary operation of the inverse are continuous with respect to this global L-neighborhood structure. Some examples of global L-neighborhood groups are given. It is shown that the L-topological groups, given by Ahsanullah in 1984 and later by Bayoumi in 2003, are special global L-neighborhood groups. We also show that all initial and final lifts and hence all initial and final global L-neighborhood groups uniquely exist in the category L-GnghGrp of global L-neighborhood groups. These initial and final global L-neighborhood groups are defined using the initial and final global L-neighborhood structures. Moreover, we show that the L-neighborhood groups, defined by Ahsanullah using the L-neighborhood structures in sense of Lowen, are special global L-neighborhood groups, for L=I is the closed unit interval.